Given are twenty-two different five-element sets, such that any two of them have exactly two elements in common. Prove that they all have two elements in common.
Source: Russian TST 2014, Day 10 P1 (Group NG)
Tags: combinatorics, set theory
Given are twenty-two different five-element sets, such that any two of them have exactly two elements in common. Prove that they all have two elements in common.